Moment-Based Estimation of State-Switching Rates in Cell Populations

2022

Preprint

Self Cite

We consider a fluctuation test experiment in which cell colonies are grown from a single cell until they reach a given population size, and then they are exposed to treatment. While they grow, the cells may, with a low probability, acquire resistance to treatment and pass it on to their offspring. Unlike the classical Luria-Delbrück fluctuation test and motivated by recent work on drug-resistance acquisition in cancer/microbial cells, we allow for the resistant cell state to switch back to a drug-sensitive state. This modification does not affect the central part of the (Luria-Delbrück) distribution of the number of resistant survivors: the previously developed approximation by the Landau probability density function applies. However, the right tail of the modified distribution deviates from the power law decay of the Landau distribution. We demonstrate that the correction factor is equal to the Landau cumulative distribution function.

Section: Discussionmentioning

confidence: 79%

“…Conditioning on a fixed population thus eliminates the proliferation noise. Another approach to this consists in calculating the relative fractions of sensitive/resistant cells [8].…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Then the mean resistant fraction satisfies ∑ N m=0 mP N (m)/N = µ/(µ + λ), i.e. it does not change as the population grows [8].…”

Section: Stochastic Initial Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reversibility of resistance in a fluctuation test experiment modifies the tail of the Luria-Delbrück distribution

Bokes

Hlubinová

2022

Preprint

Self Cite

Probing transient memory of cellular states using single-cell lineages

Saint-Antoine

2023

Front. Microbiol.

Self Cite

The inherent stochasticity in the gene product levels can drive single cells within an isoclonal population to different phenotypic states. The dynamic nature of this intercellular variation, where individual cells can transition between different states over time, makes it a particularly hard phenomenon to characterize. We reviewed recent progress in leveraging the classical Luria–Delbrück experiment to infer the transient heritability of the cellular states. Similar to the original experiment, individual cells were first grown into cell colonies, and then, the fraction of cells residing in different states was assayed for each colony. We discuss modeling approaches for capturing dynamic state transitions in a growing cell population and highlight formulas that identify the kinetics of state switching from the extent of colony-to-colony fluctuations. The utility of this method in identifying multi-generational memory of the both expression and phenotypic states is illustrated across diverse biological systems from cancer drug resistance, reactivation of human viruses, and cellular immune responses. In summary, this fluctuation-based methodology provides a powerful approach for elucidating cell-state transitions from a single time point measurement, which is particularly relevant in situations where measurements lead to cell death (as in single-cell RNA-seq or drug treatment) or cause an irreversible change in cell physiology.

Reversible Transitions in a Fluctuation Assay Modify the Tail of Luria–Delbrück Distribution

Bokes

Hlubinová

2023

Axioms

We consider a fluctuation test experiment in which cell colonies were grown from a single cell until they reach a given population size and were then exposed to treatment. While they grow, the cells may, with a low probability, acquire resistance to treatment and pass it on to their offspring. Unlike the classical Luria–Delbrück fluctuation test, and motivated by recent work on drug-resistance acquisition in cancer/microbial cells, we allowed the resistant cell state to switch back to a drug-sensitive state. This modification did not affect the central part of the Luria–Delbrück distribution of the number of resistant survivors: the previously developed approximation by the Landau probability density function applied. However, the right tail of the modified distribution deviated from the power law decay of the Landau distribution. Here, we demonstrate that the correction factor was equal to the Landau cumulative distribution function. We interpreted the appearance of the Landau laws from the standpoint of singular perturbation theory and used the asymptotic matching principle to construct uniformly valid approximations. Additionally, we describe the corrections to the distribution tails in populations initially consisting of multiple sensitive cells, a mixture of sensitive and resistant cells, and a cell with a randomly drawn state.